The only character I gave mechanical validation was Inciniroar as his playstyle is commonplace in other fighting games but unique to it in Smash. My argument for the Pokémon Trainer was that, as the series recurring main protagonist he has to have his spot on the roster in order to have a perfect representation of the Pokémon series. They may not be the mascot of the series but they're still just as important to the series as Link, Samus, or Marth. Squirtle and Ivysaur are important to the character as well not only from a mechanical standpoint (that you don't care about for some reason) but because they also represent the journey that the player undergoes in every Pokémon game. They start with a stage one starter Pokémon (Squirtle), and as they progress their Pokémon gets stronger and evolves (Ivysaur) until they are an unstoppable powerhouse (Charizard) at the end of the game.
First, it doesn't matter if a particular archetype is common in other fighting games; that doesn't mean that it has to be in Smash or even that it's a good fit for Smash.
For PT, it's not that I don't care about the Pokémon mechanics he/she represents; rather, I don't think that those things are worth creating two additional uniques and throwing off the balance in the representation. Having PT make a cameo in the background for certain Pokémon characters like Charizard is fine if you really want him/her to appear in some form. I guess I'd be okay with a PT that uses mons from different Gens, but at the same time there aren't many great choices for that. Oshawott, for example, is hard to justify when Zoroark is the de facto face of Gen 5. You could just decide not to restrict yourself to starters and use other Pokémon to fill the three slots, but at that point you might as well just make them all separate characters. And I also get that the Squirtle and Ivysaur help represent the stages of a Pokémon journey, but my earlier argument was that this already has a sort of "soft" representation with other mons in Smash. For example, Lucario is a Stage 1, Greninja is a Stage 2, and Jiggs and Pikachu are in their base form (unless you count the babies, but even then these two aren't in their final form). Is this as good as PT's representation of the stages? No, but it's close enough that I'm not making two full uniques just to make it a tiny bit better.
You could also make the argument that PT is there in an abstract sense when you play as a Pokémon in Smash; that is, the Smash player himself/herself is kinda acting as the Trainer in a way. My understanding is that (story-wise) most Pokémon don't know how to battle properly unlesss they have a trainer, so fighting with a Pokémon in Smash is kinda like you're the trainer telling, say, Pikachu what to do. Maybe not the best argument, but it's something.
I can see where you're coming from but I personally can't justify cutting characters for the sole purpose of replacing them.
Why not? If a character being cut allows for something better in its place, it's a net gain. This is especially the case when you have stuff like Greninja or Incineroar who are pretty much just there for promotion and little else; when they're no longer promoting anything, they could be canned, unless their legacy has grown large enough since their inclusion that they are worth keeping for other reasons. Incineroar in particular I don't see building a significant legacy, but I guess we'll have to wait and see on that.
Personally, I think if it has to be mostly Gen 1 representation, then let it. That’s where most of the iconic Pokémon are from.
Yeah, not every Gen necessarily has to have a rep. Most people wouldn't say we need a rep from every single Zelda game or every single FE continent.
I wouldn't want it to be all Gen 1, as you ought to have at least a couple from later Gens, but it's hard to find many mons that can outdo Pikachu, Mewtwo, and Charizard. Besides, you can still get Zard, for example, as a second starter and Mega Forme in Gen 6 which is pretty recent. And even without that he's still incredibly well-known. It's not like Zard is any less "relevant" than Incineroar.